1. Field of the Invention
The present invention relates to a system for grid convergence solution computation and a method for the same, and, more specifically, to grid convergence solution computation system and method capable of being effectively used for determining the airfoil cross section of, for example, a rotor blade for a rotary-wing aircraft.
2. Description of the Related Art
Computational fluid dynamics (CFD) capable of working out solutions to fluid-dynamic problems by numerically solving fluid-dynamic governing equations using a computer has made a rapid progress in recent years. A desired airfoil cross section of a rotor blade of a rotary-wing aircraft is predicted analytically by CFD prior to determining the airfoil cross section through wind tunnel tests and actual aircraft tests.
FIG. 8 is a graph showing the relation between the number of grids and drag coefficient for a typical two-dimensional cross section of a middle part of an airfoil determined through CFD analysis. As shown in FIG. 8, the drag coefficient CD varies in an asymptotic curve gradually approaching a predicted grid convergence solution represented by a line L1 with increase of the number of grids. A grid convergence solution corresponds to a solution obtained when the meshes of grid are reduced to a limit. The smaller the meshes of a computation grid, the smaller is the error in the computed convergence solution. Practically, computers have a limited processing ability and, in many cases, are unable to deal with a necessary and sufficient number of computation grids and are unable to achieve computation in a satisfactorily high computational accuracy.
FIG. 9 is a pictorial view of a coarse numerical grid for the computation of airfoil flows displayed on a screen 1 of a display. FIG. 10 is a pictorial view of a fine numerical grid for the computation of airfoil flows displayed on a screen 1 of a display. FIG. 11 is a flow chart of a conventional computation system of computing a grid convergence solution and errors. A practically applied conventional computation system uses a coarse grid and a fine grid, and predicts the grid convergence solution from computed values obtained through computations using the numerical grids.
Referring to FIGS. 9 to 11, the computation system generates a coarse grid in step s1 executes computations using the coarse grid in step s2, provides a computed value Ac in step s3, and then goes to step s7. On the other band, the computation system generates a fine grid in step s4, executes computations using the fine grid in step s5, provides a computed value Af in step s6, and then goes to step s7. In step s7, a query is made to see if the absolute value of the difference between the computed values A, and A_is sufficiently small. If the response in step s7 is affirmative, the computed value Ac is decided to be sufficiently approximate to a grid convergence solution in step s8. If the response in step s7 is negative, it is considered that the absolute value of the difference between the computed values Ac and Af is a predicted error. Then, in step s9, a grid convergence solution is predicted on the basis of the predicted error and the computed values Ac and Af.
This conventional computation system needs much work time for generating the plurality of types of grids, i.e., the coarse grid and the fine grid, for a computational space of a complicated shape. The conventional computation system is unable to use a very fine grid because there is a limit to the processing ability of the computer. The use of an excessively coarse grid reduces computation accuracy extremely. Thus, mesh sizes of practically usable grids are in a relatively narrow range. Therefore, the conventional computation system has a practical difficulty in accurately predicting a grid convergence solution and there is a limit to the conventional computation system in dealing with computational spaces having complicated shapes.